解方程3条x^2-2x-1=02y^2+y-1=02logx 25-3log25 x=1

解方程3条x^2-2x-1=02y^2+y-1=02logx 25-3log25 x=1
解方程3条
x^2-2x-1=0
2y^2+y-1=0
2logx 25-3log25 x=1

解方程3条x^2-2x-1=02y^2+y-1=02logx 25-3log25 x=1
x^2-2x-1=0
x^2-2x=1
x^2-2x+1=1+1
(x-1)^2=2
x-1=√2或x-1=-√2
x1=√2+1 x2=-√2+1
2y^2+y-1=0
(y+1)(2y-1)=0
y1=-1 y2=1/2
2lg25/lgx -3lgx/lg25=1
令t=lgx,则
2lg25/t-3t/lg25=1
两边乘以t*lg25,
2lg25*lg25-3t^2-t*lg25=0
3t^2+t*lg25-2lg25*lg25=0
(t+lg25)(3t-2lg25)=0
t=-lg25或t=2/3*lg25
lgx=-lg25或lgx=2/3lg25
x=1/25或x=25^2/3

x^2-2x-1=0
（x-1)²=2
x-1=√2或x-1=-√2
x1=1+√2 x2=1-√2
2y^2+y-1=0
(y+1)(2y-1)=0
y1=-1 y2=1/2
2logx 25-3log25 x=1
设log25 x=y，则logx 25=1/y
2/y-3y=1
3y²...

全部展开

x^2-2x-1=0
（x-1)²=2
x-1=√2或x-1=-√2
x1=1+√2 x2=1-√2
2y^2+y-1=0
(y+1)(2y-1)=0
y1=-1 y2=1/2
2logx 25-3log25 x=1
设log25 x=y，则logx 25=1/y
2/y-3y=1
3y²+y-2=0
(3y-2)(y+1)=0
y=2/3 y=-1
当y=2/3时，log25 x=2/3, x=5倍3次根号5
当y=-1时，log25 x=-1, x=1/25

收起